Vectorization techniques have proved to be extremely effective for large-scale reservoir simulations. Parallel capabilities hold even greater potential for these enormous problems. Domain decomposition methods can allow the physical problem to be divided up into many similar problems that can be addressed separately, in parallel, on different processors. These techniques also allow efficient application of local grid refinement to resolve the important local phenomena that may govern the flow process. Eulerian-Lagrangian methods that follow the flow also can profit extensively from parallel treatment of the characteristics of the flow. The effectiveness of these techniques will be demonstrated on research codes and illustrative applications.